A local Whittle estimator is developed to simultaneously estimate the long memory parameters for stationary anisotropic scalar random fields. It is shown that these estimators are consistent and asymptotically normal, under some weak technical conditions. A brief simulation study illustrates a...

A weighted multivariate signed-rank test is introduced for an analysis of multivariate clustered data. Observations in different clusters may then get different weights. The test provides a robust and efficient alternative to normal theory based methods. Asymptotic theory is developed to find...

The aim of this paper is to present a framework for asymptotic analysis of likelihood ratio and minimum discrepancy test statistics. First order asymptotics are presented in a general framework under minimal regularity conditions and for not necessarily nested models. In particular, these...

Multivariate mode hunting is of increasing practical importance. Only a few such methods exist, however, and there usually is a trade-off between practical feasibility and theoretical justification. In this paper we attempt to do both. We propose a method for locating isolated modes (or better,...

A general approach for developing distribution-free tests for general linear models based on simplicial depth is presented. In most relevant cases, the test statistic is a degenerated U-statistic so that the spectral decomposition of the conditional expectation of the kernel function is needed...

Models for Markov processes indexed by a branching process are presented. The new class of models is referred to as the branching Markov process (BMP). The law of large numbers and a central limit theorem for the BMP are established. Bifurcating autoregressive processes (BAR) are special cases...

In this paper, some nonparametric approaches of density function estimation are developed when censoring indicators are missing at random. A conditional mean score based estimator and a mean score estimator are suggested, respectively. The two estimators are proved to be asymptotically normal...

We consider semimartingales with jumps that have finite Lvy measures. The purpose of this article is to estimate integral-type functionals of the Lvy measures from discrete observations. We propose two types of estimators: kernel-type and empirical-type estimators, both of which are obtained by...

This paper examines asymptotic expansions of test statistics for dimensionality and additional information in canonical correlation analysis based on a sample of size N=n+1 on two sets of variables, i.e., and . These problems are related to dimension reduction. The asymptotic approximations of...

Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constraints on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions into...